New approaches to determine the interface height of fire smoke based on a three-layer zone model and its verification in large confined space

Large confined space has high incidence of fires, which seriously threatens the safety of people working there. Understanding the distribution of smoke in such large space is critical to fire development prediction and smoke control. Three improved methods for the stratification interface prediction of fire smoke are developed, including of improved intra-variance, integral ratio and N-percentage methods. In these methods, the interface height is determined by the vertical temperature distribution based on a three-layer smoke zone model, which is an improvement of a two-layer zone model. Thereafter, the three improved methods are applied to several typical fire cases simulated CFD to predict the smoke interface, and their applicability and reliability are verified by comparison of the smoke stratification results with the filed simulation results. Results show that the three improved methods can effectively determine the location of the three-layer zone model's interface, and they have the ability to predict smoke interface for fires with different fire source types and ventilation conditions.     

On the evaluation of a ‘time constant’ for studying the smoke-filling processes in atrium spaces

The time constant which has been previously proposed to characterize the smoke-filling time in an atrium space for design purposes is further evaluated in this paper using the CFAST, FAST and CCFM. VENTS zone models developed at the Building and Fire Research Laboratory, NIST, USA. A design fire of thermal power and area related to the volume of the atrium space is proposed in order to evaluate the time constant. Results of the zone-modelling simulation supported the fact that the time required to fill 80% of the atrium space with smoke is related to its time constant. Full-scale experimental results on smoke-filling processes in atria available in the literature are compared. Use of this quantity to specify the smoke-filling time for an atrium space is recommended for design purposes.     

Use of zone models on simulating compartmental fires with forced ventilation

Performance of three fire zone models BR12, CCFM.VENTS and CFAST in simulating forced ventilation fires with low heat release and high ventilation rates were studied experimentally. A fire chamber of length 4.0 m, width 3.0 m height 2.8 m with adjustable ventilation rates was used. Burning tests were carried out with wood cribs and methanol to study the preflashover stage of a compartmental fire and the effect of ventilation. The mass loss rate of fuel, temperature distribution of the compartment and the air intake rate were measured. The heat release rates of the fuel were calculated from the measured mass loss rate. The smoke temperature was used as the validation parameter. A scoring system is proposed to compare the results predicted by the three models. An empirical expression for calculating the smoke temperature is assessed. Lastly, the Computational Fluid Dynamics technique is also used for comparing the simulated fire environment.     

Modelling thermal degradation of composite materials

A one–dimensional, transient thermal degradation heat transfer model for the response of composite materials when exposed to fire is presented. The model can handle layers of different materials. Material properties are functions of temperature. The reaction can be specified using Arrhenius‐type parameters or by inputting a density–temperature relationship determined by any experimental technique such as thermogravimetric analysis. The model is validated against the experimental data presented in Boyer's 1984 dissertation. Overall, the model provides excellent agreement with the experimental data. It is shown that very little difference is found between results arrived at by Arrhenius kinetics and results obtained by specifying the easier to measure density–temperature relationship. From this it is concluded that this technique is a viable alternative to Arrhenius‐type models. Copyright © 2006 John Wiley & Sons, Ltd.     

Fire behaviour of timber surfaces with perforations

Timber surfaces with perforations are unfavourable from a fire design point of view, since the perforations increase the surface area exposed to fire and facilitate an increased penetration of heat into the burning zone. This can lead to an increased burning rate in comparison with heavy timber surfaces. In order to enlarge the theoretical and experimental background of the fire behaviour of timber surfaces with perforations, a series of fire tests was performed on timber assemblies made of hollow core elements with acoustic perforations and sound absorbers placed behind the perforated acoustic layer. This type of element is commonly used to improve ceiling sound absorption. The first part of the paper describes the results of the fire tests, in the second part a simplified calculation model for the burning rate is presented and compared with the test results. The model takes into account two different charring phases, before and after the perforated acoustic layer is completely charred. Good agreement between the test results and prediction of the calculation model is observed. Further the fire tests clearly showed that the charring rate during the first phase is mainly influenced by the size and the position of the perforations as well as the thickness of the perforated acoustic layer. A correlation between the charring rate and these parameters is also presented and compared with the test results. Copyright © 2004 John Wiley & Sons, Ltd.     

液化石油气储罐在喷射火焰作用下的热响应模型

Abstract This paper describes a mathematical model developed to study the behavior of liquefied petroleum gas (LPG) tanks when subjected to jet fire. The model consists of a number of field and zone sub-models which are used to simulate the various physical phenomena taking place during the tank engulfment period. The model can be used to predict the pressure and temperature of the LPG in the tank, the temperature of the wall of tank, and the time of tank explosion. The comparisons between the model predicted results and the test data show good agreement. The results show that the jet fire partially impinging on tank wall led to higher wall temperature and the time to failure was shorter than that in engulfing pool fire. And the exposure of the upper wall in the vapor zone to the fire is more dangerous than that of the LPG contacted wall.     

Comparing simple and advanced tools for structural fire safety engineering

The present paper gives an overview of the actual tools available for the estimation of the fire development and of the resulting thermal actions on structural members. A case study is developed on the basis of the Fire Safety Engineering methodology, respectively with two different approaches, one based on ‘advanced’ tools and another one based on ‘simplified’ tools. Indeed, three categories of fire models are used in this study, each of which corresponding to a different level of precision and complexity: hand calculations, zone models, and computational fluid dynamics (CFD) models. The case study is relative to the calculation of the heating of a portal frame in a gymnasium, under localised real fire conditions. It is shown through comparisons that, in this case, predictions of analytical methods are, to certain extent, in good agreement with predictions of the CFD model. In particular, it is demonstrated the relevance of using a simplified method of EN 1991‐1‐2 to predict thermal actions to vertical members. The obtained results also highlight the need to develop more relevant analytical methods in order to predict the temperature field during a fire in a large volume. Copyright © 2014 John Wiley & Sons, Ltd.     

A simplified analytical approach for the clear height in compartment fire based on a two-layer zone model

Compartment fire is an important research area in fire science and fire safety. Owing to its simplicity, the zone model remains attractive in studying compartment fire. Although computer software packages for the two-layer zone are in popular use, a basic understanding of the physical phenomena involved and the mathematical formulation thereon would benefit users of the zone model in terms of critical judgement of software outputs, which could be unreasonable, and insight of the general trends of important variables. In general, the differential equations based on a two-layer zone model have no analytical solutions and numerical methods are required. However, stiffness is present in using numerical methods to solve these differential equations, and reliable results are obtained only when very small time steps are used in computation. Nevertheless, in some special cases, analytical solution for the clear height in the zone model exists, as demonstrated in the present study. Predicted values of smoke layer height in the present approach are shown to be in good agreement with experimental results reported in the literature. The present work would provide insight into the tenability condition of a compartment on fire and is an important issue in fire safety management.     

Reconstruction of Grenfell Tower fire. Part 3—Numerical simulation of the Grenfell Tower disaster: Contribution to the understanding of the fire propagation and behaviour during the vertical fire spread

The dramatic event of the Grenfell Tower (June 2017), involving a combustible façade system, has raised concerns regarding the fire risk that these systems address. Indeed, as façades are complex systems, it is not straightforward to assess which part of the system is involved in the global fire behaviour. Understanding such façade fires is thus very complex as it depends on a combination of various products and system characteristics, including window frames or air gap or cavity barriers. Fire development inside the initial apartment was investigated using an appropriate CFD model with different scenarios for the fire source and ventilation conditions in a previous study. Fire propagation through the window to the external façade and to higher apartments was modelled and validated against visual observations. This paper describes CFD modelling of the complete Grenfell tower facade, and investigates vertical fire spread behaviour over the full height façade from the initial apartment. Contributions from the combustion of all the apartments' furniture, depending on window failure, and architectural details of the refurbished façade are considered in the numerical model. The modelling results are validated by comparison with photographic and video observations of the real fire.     

Reconstruction of Grenfell Tower fire. Part 2: A numerical investigation of the fire propagation and behaviour from the initial apartment to the façade

The dramatic event of the Grenfell Tower in 2017 reminds the importance of addressing fire issues as a whole and clearly highlighted one of the major roles played by the façade as fire propagation vector. To understand and analyse this disaster, numerical simulation allows particular phenomena to be evaluated more easily. The numerical model addressed for the fire behaviour of the façade system was developed using a multiscale approach and validated at different scales. In this paper, the fire behaviour of the façade and of its window frames is addressed. A computational fluid dynamics (CFD) model is used to investigate the fire spread from the initial apartment to the overall façade with different scenarios for the fire source and ventilation. Fire propagation through windows to the façade and to upper apartments is addressed. General curves representing the re-entry of flames into upper apartment are extracted from simulations. The numerical results are validated by comparison with observations from videos and pictures of the real fire. Numerical results show that whatever the initial fire location and ventilation conditions, even if the fire source is of hundreds kilowatts, it is enough to ignite the adjacent element early and to the appearance of external flames shortly after.     

Soil Clean Up by in-situ Aeration. I. Mathematical Modeling

Abstract

Mathematical models are developed suitable for use in evaluating the feasibility of in-situ vapor stripping approaches for selected chemicals and site-specific environments. These models simulate the operation of both laboratory soil stripping columns and field-scale vacuum extraction wells (vent pipes). The effect of an anisotropic Darcy's constant is examined and the compressibility of the extracting gas is taken into account. The models incorporate the assumption of local equilibrium for the volatile compounds between the condensed and vapor phases. These models may use Henry's law or more complex isotherms for this equilibrium. A method is developed for calculating Henry's constant from field analytical data, and it is noted that use of Henry's constants calculated from laboratory data on solutions of volatile solutes in pure water can lead to very serious errors. It is shown that evacuation wells should be screened only down near the impermeable layer beneath the zone of stripping (unsaturated zone) for most efficient functioning     

Three‐dimensional solution for the vibration analysis of functionally graded multiwalled carbon nanotubes/phenolic nanocomposite cylindrical panels on elastic foundation

In this study, based on the three‐dimensional theory of elasticity, free vibration characteristics of nanocomposite cylindrical panels reinforced by multiwalled carbon nanotubes (MWCNT) are considered. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin–Tasi equation was used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin–Tsai equation from expressing a straight line to a nonlinear one in the MWNTs wt% range considered. Symmetric and asymmetric volume fraction profiles are provided in this article for comparison. It is shown that using only few grid points, accurate results are obtained which demonstrate the efficiency and convenience of the generalized differential quadrature method for the problem under consideration. The validity of the Young's modulus and frequency response were assessed by a comparison with available literature data, providing a good agreement. POLYM. COMPOS., 34:2040–2048, 2013. © 2013 Society of Plastics Engineers     

ANALYTICAL SOLUTIONS FOR THE MOVING INTERFACE PROBLEM IN FREEZE-DRYING WITH OR WITHOUT BACK HEATING

ABSTRACT

A mathematical model for freeze-drying without back surface heating is established first in this paper by a combination of URIF (uniformly retreating ice front) and Sheng/Peck's theories. Explicit analytical expressions are obtained for the rates of interface movement and drying. The predicted drying rate and temperature profile are in good agreement with the Sheng/Peck's model results. Furthermore, the model is extended to the process of freeze-drying with back heating in which the temperature at the interface is assumed to increase along the path of movement. It is shown that the average rates for drying and interface moving may be obtained by assuming a quadric distribution for the interface temperature.     

Contrast attenuation coefficient as a parameter enabling determination of range of visibility in smoke

The contrast attenuation coefficient characterizes smoke production properties of a material. These properties are closely connected with a contrast of luminance of a scene observed in a smoky medium, the range of visibility, and mass concentration in an environment volume. The range of visibility determines a person's chances of moving about in a fire zone. This paper presents considerations on conditions of visibility in smoky compartments, a method of the contrast attenuation measurement and test results for some materials. © 1997 John Wiley & Sons, Ltd.     

The Model of Thermal Response of Liquefied Petroleum Gas Tanks Partially Exposed to Jet Fire

This paper describes a mathematical model developed to study the behavior of liqupfied petroleum gas (LPG) tanks when subjected to jet fire. The model consists of a number of field and zone submodels which are used to simulate the various physical phenomena taking place during the tank engulfment period. The model can be used to predict the pressure and temperature of the LPG in the tank, the temperature of the wall of tank, and the time of tank explosion. The comparisons between the model predicted results and the test data show good agreement. The results show that the jet fire partially impinging on tank wall led to higher wall temperature and the time to failure was shorter than that in engulfing pool fire. And the exposure of the upper wall in the vapor zone to the fire is more dangerous than that of the LPG contacted wall.     

A numerical study of gypsum plasterboard behaviour under standard and natural fire conditions

Gypsum plasterboards are the most widely used passive fire protection for timber structures, especially in the case of light timber frame construction. Understanding the complex thermo‐physical behaviour of plasterboard at elevated temperature is vital in the performance‐based design of any structure adopting gypsum as passive fire protection (PFP). Numerous heat transfer studies have been conducted over the years where attempts have been made to simulate the fire performance of gypsum‐protected assemblies, subject to standard fire exposure. However, contradictory thermal properties for gypsum plasterboard are apparent throughout. As a result, it is unclear from a practitioner's perspective as to which studies represent reasonable properties for design purposes. In recognition of this the authors present a numerical study highlighting the consequences of adopting many of the differing property sets available in the literature, the sensitivity of temperature development resulting from deviations from the assumptions that underpin such properties, and the consequences of adopting plasterboard properties derived from standard fire tests, in natural fire situations. The study presents heat transfer simulations conducted using the finite element software TNO DIANA coupled with both laboratory and natural fire tests conducted on Structural Insulated Panels (SIPs) and Engineered Floor Joists (EFJs). It is found from this study that plasterboard properties are highly sensitive to the assumed free and chemically bound moisture contents. Minor percentage changes are shown to have a significant influence on the temperature development of SIPs exposed to standard furnace fires, while some of the most accepted plasterboard properties available in the literature are found, in some cases, to be non‐conservative when adopted in simulations of SIPs. More interestingly, it is also found that the properties of plasterboard available in the literature, largely derived from standard fire tests, are not independent of the heating rate. As a result, when such properties are applied to natural fire problems significant inaccuracies can occur. Copyright © 2011 John Wiley & Sons, Ltd.     

Deformation and fracture of adhesive layers constrained by plastically-deforming adherends

The use of an embedded-process zone (EPZ) model to investigate the mode I cohesive parameters for plastically-deforming, adhesively-bonded joints is demonstrated in this paper. It is shown that for the particular systems investigated, the cohesive parameters are consistent with an adhesive layer deforming in accordance with its bulk constitutive properties (as constrained by the adherends). In other words, these systems provide examples where the cohesive tractions exerted by an adhesive layer can be calculated simply from considerations of the constrained deformation of the adhesive. Consistent with such calculations, the peak stress in the adhesive layer decreases as the level of the constraint decreases (either with an increase in the thickness of the adhesive layer or with a decrease in the thickness of the adherends). It is also shown that owing to a compensating effect in which the critical displacement for failure varies with the constraint, the energy absorbed by the adhesive layer (the 'intrinsic' toughness of the joint) is essentially independent of the geometry in these systems.     

Modified carbon‐dioxide measurement to predict the heat release rate of fire burning in a compartment based on the three‐zone model

The heat release rate (HRR) of fuels has been described as the single important variable of fuels in fire hazard, and the HRR experimental measurement remains a key issue in fire science. A modified carbon‐dioxide generation (CDG) method, applying a three‐zone smoke model, is developed to predict the HRR of gas, liquid, and solid fuel fires. The three‐zone smoke model with three layers is determined by the vertical thermal stratification, and their physical thermal properties are computed. The application of modified method on typical gas fuel, liquid fuel, and simple solid‐fuel fires is verified. The prediction accuracy is examined quantitatively by the cosine similarity comparison of predicted results with the experimental data. In addition, the ventilation effects on the predicted results are also explored. Results show that the application of three‐zone model improves the HRR prediction accuracy, because it can accurately capture the mixing behavior from the upper layer to the lower layer. The effect of ventilation on modified CDG method is positive as the ventilation enhances the smoke mixing and the smoke distribution in each layer is relatively uniform.     

Evaluation of the room smoke filling time for fire plumes: Influence of the room geometry

The article examines numerically and theoretically the effects of room aspect ratio on the fire smoke filling process. It aims to evaluate the two-zone models used in fire safety engineering to predict the smoke filling times. Using Fire Dynamics Simulator, numerical simulations are performed and compared to a simplified zone model. The results show that the two-zone model overestimates the smoke filling time in the case of a compartment with a large surface area. To improve the predictions of two-zone models, simple correlations are established for the duration of the phenomena occurring before the formation of a two-layer stratification in a fire compartment. These new correlations allow the zone model to be significantly improved.     

Parameter Estimation Under Failure-Censored Constant-Stress Life Testing Model: A Bayesian Approach

Abstract

This article compares likelihood and Bayesian estimations for partially accelerated constant-stress life test model under type II censoring assuming Pareto distribution of the second kind. Both maximum likelihood and Bayesian estimators of the model parameters are derived. The posterior means and posterior variances are obtained under the squared error loss function using Lindley's approximation procedure. The advantages of this proposed procedure are shown. Monte Carlo simulations are conducted under different samples sizes and different parameter values to assess and compare the proposed methods of estimation. A noninformative prior on the model parameters is used to make the comparison more meaningful. It has been observed that Lindley's method usually provides posterior variances and mean squared errors smaller than those of the maximum likelihood estimators. That is, Lindley's method produces improved estimates, which is an advantage of this method.